Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 PDF Download
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Author: Walter Edwin Sewell
Publisher: Princeton University Press
ISBN: 1400882214
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.
Author: Walter Edwin Sewell
Publisher: Princeton University Press
ISBN: 1400882214
Category : Mathematics
Languages : en
Pages : 248
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Book Description
The description for this book, Degree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9, will be forthcoming.
Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426
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Book Description
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Author: Joseph L. Walsh
Publisher: Springer Science & Business Media
ISBN: 9780387987828
Category : Mathematics
Languages : en
Pages : 734
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Book Description
This volume is a selection from the 281 published papers of Joseph Leonard Walsh, former US Naval Officer and professor at University of Maryland and Harvard University. The nine broad sections are ordered following the evolution of his work. Commentaries and discussions of subsequent development are appended to most of the sections. Also included is one of Walsh's most influential works, "A closed set of normal orthogonal function," which introduced what is now known as "Walsh Functions".
Author: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418
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Book Description
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.
Author: Sorin G Gal
Publisher: World Scientific
ISBN: 9814466972
Category : Mathematics
Languages : en
Pages : 350
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Book Description
The monograph, as its first main goal, aims to study the overconvergence phenomenon of important classes of Bernstein-type operators of one or several complex variables, that is, to extend their quantitative convergence properties to larger sets in the complex plane rather than the real intervals. The operators studied are of the following types: Bernstein, Bernstein—Faber, Bernstein-Butzer, q-Bernstein, Bernstein-Stancu, Bernstein-Kantorovich, Favard-Szász-Mirakjan, Baskakov and Balázs-Szabados.The second main objective is to provide a study of the approximation and geometric properties of several types of complex convolutions: the de la Vallée Poussin, Fejér, Riesz-Zygmund, Jackson, Rogosinski, Picard, Poisson-Cauchy, Gauss-Weierstrass, q-Picard, q-Gauss-Weierstrass, Post-Widder, rotation-invariant, Sikkema and nonlinear. Several applications to partial differential equations (PDEs) are also presented.Many of the open problems encountered in the studies are proposed at the end of each chapter. For further research, the monograph suggests and advocates similar studies for other complex Bernstein-type operators, and for other linear and nonlinear convolutions.
Author: GAIER
Publisher: Springer Science & Business Media
ISBN: 1461248140
Category : Mathematics
Languages : en
Pages : 207
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Book Description
The theory of General Relativity, after its invention by Albert Einstein, remained for many years a monument of mathemati cal speculation, striking in its ambition and its formal beauty, but quite separated from the main stream of modern Physics, which had centered, after the early twenties, on quantum mechanics and its applications. In the last ten or fifteen years, however, the situation has changed radically. First, a great deal of significant exper~en tal data became available. Then important contributions were made to the incorporation of general relativity into the framework of quantum theory. Finally, in the last three years, exciting devel opments took place which have placed general relativity, and all the concepts behind it, at the center of our understanding of par ticle physics and quantum field theory. Firstly, this is due to the fact that general relativity is really the "original non-abe lian gauge theory," and that our description of quantum field in teractions makes extensive use of the concept of gauge invariance. Secondly, the ideas of supersymmetry have enabled theoreticians to combine gravity with other elementary particle interactions, and to construct what is perhaps the first approach to a more finite quantum theory of gravitation, which is known as super gravity.
Author: Pavel Kondratʹevich Suetin
Publisher: American Mathematical Soc.
ISBN: 9780821830000
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Discusses orthogonal polynomials.
Author:
Publisher: American Mathematical Soc.
ISBN: 9780821896327
Category : Mathematical analysis
Languages : en
Pages : 292
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Book Description
Author: John Hamilton Curtiss
Publisher:
ISBN:
Category : Interpolation
Languages : en
Pages : 70
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Book Description
Let Hn (u;z) denote the harmonic polynomial of degree at most n found by interpolation in 2n +1 points in a function u given on the boundary C of a region D of the complex z-plane. Explict formulas are derived for Hn in the case of interpolation on a circle and on an ellipse, and convergence is proved in these cases for arbitrary continuous boundary data. Various generalizations are indicated.
